Name of the highest power of 2 smaller than or equal to a given number For a number $x$, I would like to know whether there is a common name for the number $2^n$ such as $2^n \leq x < 2^{n+1}$ (e.g. If $x = 7$, then $2^n = 4$, $n = 2$).
I have some computer science related article where I extensively use such a number and I need a name to give it in order to explain how an algorithm works without having to repeat the number definition over and over every time I need to use it. I currently call it a "base $2$", saying for example that "$4$ is the base $2$ of $7$" (see example above), and that we need to "compute the base $2$ of the number", but this name feels wrong. Do you know whether a common name exists for such a number?
Note: actually, the article I am talking about deals with Gray codes. I am looking for a term that looks like it comes from math and not from computer science since many terms from computer science that deal with powers of two tend to be references to the usual binary representations of numbers. As an example, with Gray codes $2^3$ is 0b1100 and not 0b1000 so I am trying to avoid names that would literally mean the $n$th set bit, hence the question on Math.SE.
Note 2: as it has been highlighted in the many answers and comments, the goal of this question, once clearly reformulated, is to find a terse, pronounceable name for the function $2^{\lfloor \log_2(x) \rfloor}$ so that it is possible to say that "some number is the [insert name here] of $x$".
 A: You could call it $2^{\lfloor \log_2(x) \rfloor}$.
A: Moved from comment
I suggest derivations from octave or binade. These words are typically used to describe ranges spanning powers of two rather than a specific value within them, but because a power-of-two uniquely defines an octave/binade (it is its lowest value; in other words, it is a base value, or a floor), you could use the same word for both the interval and this defining value.
For instance, you could name it the binadic floor. I favour this expression because the concept of binades is clear once formulated, and the concept of floor is unambiguous and generally well-understood. The rarity of "binade" means that "binadic floor" is sufficiently unusual as to not be confused with the regular floor, and "binadic floor" rolls quite well off the tongue.
Another possibility is octaval base/root/floor, but "octave", "base" and "root" all have pre-existing connotations, and when spoken, octaval floor doesn't sound right because the -al and fl- interact poorly, forcing a break.
Let us define the binade of a positive integer $N$ as the set of integers $[2^n, 2^{n+1})$ that contains $N$, and the binadic floor of an integer $N$ as the lower bound of $N$'s binade...
A: I would just describe it as the "largest power of two not exceeding $x$". See A053644 in OEIS for other names and information.
A: I don't know a standard term, but "dyad" might be a good choice. The word roughly means "twoness", and is used for example in dyadic decompositions in a manner similar to the one you want.
A less exotic name would be "order of magnitude". (Explaining that it is with respect to base $2$.)
A: The term I have always been using for that number is x rounded down to a power of two. I can't imagine a term which would be shorter to pronounce. The shortest symbolic notation suggested in other answers, would be pronounced as two raised to the log base two of x rounded down, which is a bit longer to pronounce and harder to understand when you hear it said.
A: In the context of data structures - specifically, the van Emde Boas layout - I've heard this referred to as the hyperfloor of $x$. See “Cache-Oblivious B-Trees (Wayback Machine) by Bender, Demaine, and Farach-Colton for details - it defines the hyperfloor of $x$, denoted $\lfloor \lfloor x \rfloor \rfloor$, to be $2^{\lfloor \log_2 x \rfloor}$.
Hope this helps!
A: If $x$ is an integer, then $n+1$ is the bit length of $x$.
A: Why not something like "binary downscale", since you're basically treating the powers of two as a scale for rounding down. It's not all too descriptive, but it sounds like you want something short.
When using it, you could say "14's binary downscale is 8".
A: I might call it the "logarithmic floor", although this term is not well known (I just coined it),  It could perhaps be misinterpreted to mean $e^{\lfloor \ln x \rfloor}$ or $10^{\lfloor \log_{10} x \rfloor}$, but in the context of Gray codes I'd think base-2 would be semi-implied.
A: You're after the arithmetic value of the most significant digit of the number, when written in binary. As a digit it is always 1, of course (unless the number is zero), but if you're inventing terminology you can say "the most significant (binary) digit of 7 has value 4", and kind of make sense.
A: You could maybe use the fact that the upper end-point is twice as large as the lower end-point. Something like even interval or double interval ..
A: I think it is called Binary logarithm.
Wikipedia page:
http://en.wikipedia.org/wiki/Binary_logarithm
A: It seems like your n + 1 is the most significant bit, so maybe a good name would be the second most significant bit, or maybe the almost significant bit?
A: How about truncate? That is, you truncate all but the most significant digit to 0.
